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3 years ago

11

Brent counted 10 red cards, 10 black cards, and 20 blue cards in a deck of cards. What is the ratio of red cards to other cards?

Answers: A) 1:1 B) 1:2 C) 2:1 D) 1:3

1 answer:

Dmitrij [34]3 years ago

8 0

Answer:

1:3

Step-by-step explanation:

10 red cards, 10 black cards, and 20 blue cards

We want the ratio of red to other cards

red : blue and black

10 : 10+20

10 : 30

Divide each side by 10

10/10 : 30/10

1:3

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3 years ago

5.Footlocker buys Air Jordans for $30 a pair. They mark it up 75%. How much is the mark-up on a pair of Air Jordans

allochka39001 [22]

Answer:

$52.50

Step-by-step explanation:

What you do is you move the decimal two times to the left from 75%.

0.75*?=?

Take the orginal price and multiply ($30) by 0.75.

0.75*30= $22.50

Take 22.50 and add that to your original amount.

$22.50+$30= $52.50 or $52.5

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3 years ago

According to a human modeling project, the distribution of foot lengths of 16- to 17-year-old boys is approximately Normal wi

anygoal [31]

The percentage of boys 16- to 17-years-old who wear a size 11 shoe or larger is 3.59%.

<u>Step-by-step explanation:</u>

Step 1: Sketch the curve.

The probability that X>27.9 is equal to the blue area under the curve.

Step 2:

Since μ=25.2 and σ=1.5 we have:

P ( X > 27.9 ) = P ( X−μ > 27.9−25.2 )

⇒ P ( X−μ/σ > 27.9−25.2/1.5)

Since Z=x−μσ and 27.9−25.21.5=1.8 we have:

P ( X>27.9 )=P ( Z>1.8 )

Step 3: Use the standard normal table to conclude that:

P (Z>1.8)=0.0359

Percentage = $0.0359(100) = 3.59$ %

Therefore , The percentage of boys 16- to 17-years-old who wear a size 11 shoe or larger is 3.59%.

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3 years ago

Find the measure of a central angle that intercepts an arc of 3 inches in a circle whose radius is 8 inches.

Tresset [83]

Answer:

option (A)

central angle = 0.375 rad

Step-by-step explanation:

Given in the question,

radius of the circle = 8 inches

arc of the circle = 3 inches

To find,

measure of a central angle

Central angles are subtended by an arc between those two points.

Formula to use:

<h3> s = (r) (θ)</h3>

<em>where r = radius </em>

<em> s = arc length </em>

<em> θ = angle in radians</em>

<em />

Plug in the values in the equation

<h3>3 = (8) (θ)</h3><h3>θ = 3/8 </h3><h3>0.375 rad</h3>

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4 years ago

Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level. The null and alternative hyp

exis [7]

Answer:

$H_0: \, \mu = 2$ .

$H_1:\, \mu > 2$ .

Test statistics: $z \approx 2.582$ .

Critical value: $z_{1 - 0.025} \approx 1.960$ .

Conclusion: reject the null hypothesis.

Step-by-step explanation:

The claim is that the mean $\mu$ is greater than $2$ . This claim should be reflected in the alternative hypothesis:

$H_1:\, \mu > 2$ .

The corresponding null hypothesis would be:

$H_0:\, \mu = 2$ .

In this setup, the null hypothesis $H_0:\, \mu = 2$ suggests that $\mu_0 = 2$ should be the true population mean of GPA.

However, the alternative hypothesis $H_1:\, \mu > 2$ does not agree; this hypothesis suggests that the real population mean should be greater than $\mu_0= 2$ .

One way to test this pair of hypotheses is to sample the population. Assume that the population mean is indeed $\mu_0 = 2$ (i.e., the null hypothesis is true.) How likely would the sample (sample mean $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ ) be observed in this hypothetical population?

Let $\sigma$ denote the population standard deviation.

Given the large sample size $n = 60$ , the population standard deviation should be approximately equal to that of the sample:

$\sigma \approx s = 0.06$ .

Also because of the large sample size, the central limit theorem implies that $Z= \displaystyle \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}$ should be close to a standard normal random variable. Use a $Z$ -test.

Given the observation of $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ :

$\begin{aligned}z_\text{observed}&= \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}} \\ &\approx \frac{\overline{X} - \mu_0}{s / \sqrt{n}} = \frac{2.02 - 2}{0.06 / \sqrt{60}} \approx 2.582\end{aligned}$ .

Because the alternative hypothesis suggests that the population mean is greater than $\mu_0 = 2$ , the null hypothesis should be rejected only if the sample mean is too big- not too small. Apply a one-sided right-tailed $z$ -test. The question requested a significant level of $0.025$ . Therefore, the critical value $z_{1 - 0.025}$ should ensure that $P( Z > z_{1 - 0.025}) = 0.025$ .

Look up an inverse $Z$ table. The $z_{1 - 0.025}$ that meets this requirement is $z_{1 - 0.025} \approx 1.960$ .

The $z$ -value observed from the sample is $z_\text{observed}\approx 2.582$ , which is greater than the critical value. In other words, the deviation of the sample from the mean in the null hypothesis is sufficient large, such that the null hypothesis needs to be rejected at this $0.025$ confidence level in favor of the alternative hypothesis.

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3 years ago